Hydrological Science

Time series analysis is a popular method for forecasting future values based on past observations. There are several models used in time series analysis, including the autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) models. In this post, we'll briefly explain each model and its differences. Autoregressive (AR) Model The AR model assumes that the value of a variable at a given time point is a linear combination of its past values, plus some random error. The order of the AR model, denoted as p, refers to the number of past values used to predict the current value. For example, an AR(1) model uses only the most recent past value to predict the current value, while an AR(2) model uses the two most recent past values. The equation for an AR(p) model can be written as: y(t) = c + a1y(t-1) + a2y(t-2) + ... + ap*y(t-p) + e(t) where y(t) is the current value of the time series, y(t-i) is the value of the t...

Standard Precipitation Index (SPI) SPI is used to characterize meteorological drought on a range of timescales. On short timescales, the SPI is closely related to soil moisture, while at longer timescales, the SPI can be related to groundwater and reservoir storage. The SPI can be compared across regions with markedly different climates. It quantifies observed precipitation as a standardized departure from a selected probability distribution function that models the raw precipitation data. The raw precipitation data are typically fitted to a gamma or a Pearson Type III distribution, and then transformed into a normal distribution Key Strength of SPI   • Uses precipitation only: it can characterize drought or abnormal wetness at different times scale which corresponds to the time availability of different water resources (eg: soil moisture, snowpack, river discharge, reservoir storage)   • Less complex to calculate than PDSI Key Limitation of SPI   • As a me...